# Quasigroup based crypto-algorithms

@article{Shcherbacov2012QuasigroupBC, title={Quasigroup based crypto-algorithms}, author={Victor A. Shcherbacov}, journal={ArXiv}, year={2012}, volume={abs/1201.3016} }

Modifications of Markovski quasigroup based crypto-algorithm have been proposed. Some of these modifications are based on the systems of orthogonal n-ary groupoids. T-quasigroups based stream ciphers have been constructed.

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## 9 Citations

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## References

SHOWING 1-10 OF 85 REFERENCES

Quasigroups in cryptology

- Mathematics, Computer ScienceComput. Sci. J. Moldova
- 2009

This work reviews some known published applications of quasi- groups in cryptology and gives a review of the quasigroup, stream- cipher, secret-sharing system, and zero knowledge protocol applications.

ON SOME KNOWN POSSIBLE APPLICATIONS OF QUASIGROUPS IN CRYPTOLOGY

- Mathematics, Computer Science
- 2003

It is surveyed known (published) possible application of binary and n-ary quasigroups in cryptology. Mathematics Subject Classification: 20N05, 94A60.

n-QUASIGROUP CRYPTOGRAPHIC PRIMITIVES: STREAM CIPHERS

- Mathematics, Computer Science
- 2010

A practical implementation of these ciphers that has very good cryptographic properties is presented and is based on a design concept of mixing two ”incompatible” group operations on the set Z28.

On some quasigroup cryptographical primitives

- Computer Science, MathematicsArXiv
- 2011

Using Vojvoda approach [34] we demonstrate that cryptographical primitives proposed in [26] are vulnerable relative to chosen ciphertext attack and chosen plaintext attack. We develop proposed in…

Using quasigroups for one one secure encoding

- Computer Science, Mathematics
- 2002

A method for encrypting messages based on the properties of the quasigroups is applied guarantying a very fast implementation of AMS Mathematics Subject Classi cation A P N.

Isotopy of latin squares in cryptography

- Computer Science, Mathematics
- 2010

A new algorithm for a decision problem if two Latin squares are isotopic is presented, which has the same complexity as Miller’s algorithm, but in many practical situations is much faster.

Some Probabilistic Properties of Quasigroup Processed Strings Useful for Cryptanalysis

- Mathematics, Computer ScienceICT Innovations
- 2010

The distribution of m-tuples in an arbitrary string processed by application of quasigroup E (n)-transformation is found and it can be used for statistical attack in order to discover the original message and an algorithm for this kind of attack is given.

Quasigroup String Processing

- Mathematics, Computer Science
- 1999

It is shown that the mappings E n and D n have several useful properties suitable for many purposes in cryptography coding theory de ning and improving pseudo random generators.

Parastrophic Quasigroup String Processing

- Mathematics
- 2011

In this paper, we propose a new quasigroup string transformation based on quasigroup parastrophes. Using the proposed quasigroup string transformation, a new classification of quasigroups of order 4…

On definitions of groupoids closely connected with quasigroups

- Mathematics
- 2007

Both "existential" and "equational" definitions of binary quasigroups and groupoids closely connected with quasigroups are given. It is proved that a groupoid (Q,·) is a quasigroup if and only if all…